II. Instrumental Corrections. 



Division Errors. — The measured coordinates of any star 

 are the difference in the readings on the scale corresponding to 

 the central star, and those corresponding to the star in question. 

 Hence they depend directly on the distance between two given 

 lines on the scale. If this were perfect, an equal number of 

 divisions would represent exactly the same length, no matter 

 what part of the scale were used. That is not the case how- 

 ever, and corrections must therefore be applied to the different 

 lines, so as to reduce all measured distances to a common unit. 

 The unit selected was i/ 130th of the total length, that being 

 the number of spaces into which the scale is divided. Each 

 space equals approximately one millimeter. 



In the winter of 1896- 1897, the scale used for all the Coma 

 measurements was carefully investigated for division errors, Pro- 

 fessor Jacoby's method, described by him in the American 

 Journal of Science, Vol. I, 1896, p. 333, being followed 

 throughout. The details of the investigation are to be pub- 

 lished at a later date by the observatory ; I shall give here 

 merely a table of results. A determination of the errors had 

 been made previous to shipping the scale to America, by the 

 KaiserlicJie Normal Aichungs Kommission, at Berlin. Their 

 results are published in the Annals of the Nezv York Academy 

 of Sciences, Vol. IX, p. 206. I decided to exclude them, 

 however, as it was deemed most accurate to use only those 

 results which had been obtained under the same conditions 

 and with the same instrument as all the other observations em- 

 ployed in the reductions. Nor were the quantities as used 

 greatly affected thereby, for the two determinations agree quite 

 well, differing in no case by more than o".\i. As each star 

 was made to depend on a number of lines, the error introduced 



(81) 



